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A199854
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Primes of the form 1 + m^2 + n^2 with gcd(m,n)=1.
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0
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3, 11, 59, 83, 107, 131, 179, 227, 251, 347, 443, 467, 563, 587, 971, 1019, 1091, 1187, 1259, 1283, 1307, 1451, 1523, 1571, 1619, 1811, 1907, 1931, 2027, 2099, 2411, 2459, 2579, 2819, 2939, 2963, 3203, 3251, 3299, 3371, 3467, 3491, 3539, 3779, 3803, 3923, 3947
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OFFSET
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1,1
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LINKS
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EXAMPLE
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First such decompositions are 3 = 1 + 1^2 + 1^2, 11 = 1 + 1^2 + 3^2, 59 = 1 + 3^2 + 7^2.
First instance of several decompositions for the same prime: 131 = 1 + 3^2 + 11^2 = 1 + 7^2 + 9^2.
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PROG
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(PARI) hasform(p) = {q = p - 1; for (k = 1, q/2, if (issquare(k) && issquare(q-k) && (gcd(k, q-k)==1), return(1)); ); return(0); }
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CROSSREFS
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Cf. A056899 (when the decomposition has m=1).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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